AI proves 350-year-old conjecture with record-length proof
An AI system produced a machine-checked proof resolving a 350-year-old conjecture; the formal derivation spans billions of inference steps and terabytes of files.
A team of mathematicians and AI researchers announced this week that an artificial intelligence system produced a machine-checked proof resolving a conjecture first posed in the 17th century in number theory and combinatorics.
The researchers published the full derivation in a technical paper and uploaded machine-checkable proof files and the exact software environment to a public repository for independent inspection.
The team reports the verified proof comprises billions of elementary inference steps and that the files storing the formal derivation occupy multiple terabytes. The length reflects the level of detail required by formal proof checkers.
The project combined large-scale neural models that searched for candidate arguments with established proof assistants that check every inference step. The team describes a two-stage process: a neural-guided automated prover proposed high-level strategies and intermediate statements, then the candidates were translated into the language of a proof assistant which enforced strict syntactic and semantic rules and produced a formal certificate.
Translation and formal checking consumed the majority of the project’s computing time. The group also built a formal library encoding the necessary background mathematics and developed tools to bridge the neural prover and the proof assistant.
The conjecture had been settled in special cases over the decades but lacked a complete, formally verified proof. The AI system explored millions of candidate paths, assembled a chain of lemmas and reductions, and produced a final argument that the proof assistant accepted as logically valid.
In a written comment, the project’s lead researcher wrote, “The machine-checked proof is extremely long because every small deduction is recorded and validated.” A co-author added that the paper includes instructions for reproducing the check and lists the computational resources used during the project.
The team used proof assistants such as Coq and Lean, which require strict formalization and have been used to verify complex mathematical statements and software properties for years. The paper indicates independent teams can rerun the formal checker on the published files to reproduce the verification.
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